An improved cellular automaton method to model multispecies biofilms

Modeling interspecific competition of the microbial community during anaerobic digestion based on cellular automata and ADM1

Interspecific competition for substrate and space gives rise to considerable variation in biomass distribution within the microbial community. To study microbial community in depth, we used several research methods as sampling and analytical measurements, and developed a cellular automata (CA) model that would facilitate a description of the microbial growth process based on Anaerobic Digestion Model No. 1 (ADM1) of the International Water Association (IWA). Using the CA model, we aimed to determine whether interspecific competition occurs among acidogens, acetogens and methanogens, and to examine the influence of interspecific competition on the spatial structure of microbial communities. We found that acetogens and methanogens competed for core space, resulting in a multi-layer structure. Butyrate-degrading acetogens increased in number, resulting in inhibition of propionate-degrading acetogens. Hydrogenotrophic methanogens showed stronger competitive advantage than acetotrophic methanogens. The simulation showed that the multi-layer structure of the microbial community was formed by interspecific competition.

Modeling of Symbiotic Bacterial Biofilm Growth with an Example of the Streptococcus-Veillonella sp. System

We present a multi-dimensional continuum mathematical model for modeling the growth of a symbiotic biofilm system. We take a dual-species namely, the Streptococcus-Veillonella sp. biofilm system as an example for numerical investigations. The presented model describes both the cooperation and competition between these species of bacteria. The coupled partial differential equations are solved by using an integrative finite element numerical strategy. Numerical examples are carried out for studying the evolution and distribution of the bio-components. The results demonstrate that the presented model is capable of describing the symbiotic behavior of the biofilm system. However, homogenized numerical solutions are observed locally. To study the homogenization behavior of the model, numerical investigations regarding on how random initial biomass distribution influences the homogenization process are carried out. We found that a smaller correlation length of the initial biomass distribution leads to faster homogenization of the solution globally, however, shows more fluctuated biomass profiles along the biofilm thickness direction. More realistic scenarios with bacteria in patches are also investigated numerically in this study.

Modeling of Biofilm Growth on Fine Spherical Particles with the Use of Cellular Automata: The Influence of Cell Death and Lysis on the Biofilm Structure

The paper concerns the modeling of heterogeneous biofilm growth on fine spherical particles of such biofilm forms as, e.g., fluidized-bed bioreactors. Three discrete mathematical models based on cellular automata theory were proposed. The double-substrate kinetics of biomass growth, biomass displacement, internal and external mass transfer resistances, death and lysis of microbiological cells and biofilm detachment were taken into account. It was shown that there are no significant qualitative and quantitative differences between biofilm growth on flat and spherical particles of different radii. Computer simulations were compared with experimental observations. Qualitative and quantitative agreement areachieved if both cell death and lysis aretaken into consideration and a proper algorithm of biomass displacement is used. The value of the bacteria lysis rate coefficient was estimated.

Extracellular Polymeric Substance Production and Aggregated Bacteria Colonization Influence the Competition of Microbes in Biofilms

The production of extracellular polymeric substance (EPS) is important for the survival of biofilms. However, EPS production is costly for bacteria and the bacterial strains that produce EPS (EPS+) grow in the same environment as non-producers (EPS-) leading to competition between these strains for nutrients and space. The outcome of this competition is likely to be dependent on factors such as initial attachment, EPS production rate, ambient nutrient levels and quorum sensing. We use an Individual-based Model (IbM) to study the competition between EPS+ and EPS- strains by varying the nature of initial colonizers which can either be in the form of single cells or multicellular aggregates. The microbes with EPS+ characteristics obtain a competitive advantage if they initially colonize the surface as smaller aggregates and are widely spread-out between the cells of EPS-, when both are deposited on the substratum. Furthermore, the results show that quorum sensing-regulated EPS production may significantly reduce the fitness of EPS producers when they initially deposit as aggregates. The results provide insights into how the distribution of bacterial aggregates during initial colonization could be a deciding factor in the competition among different strains in biofilms.

A mechanistic Individual-based Model of microbial communities

Accurate predictive modelling of the growth of microbial communities requires the credible representation of the interactions of biological, chemical and mechanical processes. However, although biological and chemical processes are represented in a number of Individual-based Models (IbMs) the interaction of growth and mechanics is limited. Conversely, there are mechanically sophisticated IbMs with only elementary biology and chemistry. This study focuses on addressing these limitations by developing a flexible IbM that can robustly combine the biological, chemical and physical processes that dictate the emergent properties of a wide range of bacterial communities. This IbM is developed by creating a microbiological adaptation of the open source Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS). This innovation should provide the basis for “bottom up” prediction of the emergent behaviour of entire microbial systems. In the model presented here, bacterial growth, division, decay, mechanical contact among bacterial cells, and adhesion between the bacteria and extracellular polymeric substances are incorporated. In addition, fluid-bacteria interaction is implemented to simulate biofilm deformation and erosion. The model predicts that the surface morphology of biofilms becomes smoother with increased nutrient concentration, which agrees well with previous literature. In addition, the results show that increased shear rate results in smoother and more compact biofilms. The model can also predict shear rate dependent biofilm deformation, erosion, streamer formation and breakup.

Continuum and discrete approach in modeling biofilm development and structure: a review

The scientific community has recognized that almost 99% of the microbial life on earth is represented by biofilms. Considering the impacts of their sessile lifestyle on both natural and human activities, extensive experimental activity has been carried out to understand how biofilms grow and interact with the environment. Many mathematical models have also been developed to simulate and elucidate the main processes characterizing the biofilm growth. Two main mathematical approaches for biomass representation can be distinguished: continuum and discrete. This review is aimed at exploring the main characteristics of each approach. Continuum models can simulate the biofilm processes in a quantitative and deterministic way. However, they require a multidimensional formulation to take into account the biofilm spatial heterogeneity, which makes the models quite complicated, requiring significant computational effort. Discrete models are more recent and can represent the typical multidimensional structural heterogeneity of biofilm reflecting the experimental expectations, but they generate computational results including elements of randomness and introduce stochastic effects into the solutions.

A mechanistic Individual-based Model of microbial communities

Accurate predictive modelling of the growth of microbial communities requires the credible representation of the interactions of biological, chemical and mechanical processes. However, although biological and chemical processes are represented in a number of Individual-based Models (IbMs) the interaction of growth and mechanics is limited. Conversely, there are mechanically sophisticated IbMs with only elementary biology and chemistry. This study focuses on addressing these limitations by developing a flexible IbM that can robustly combine the biological, chemical and physical processes that dictate the emergent properties of a wide range of bacterial communities. This IbM is developed by creating a microbiological adaptation of the open source Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS). This innovation should provide the basis for "bottom up" prediction of the emergent behaviour of entire microbial systems. In the model presented here, bacterial growth, division, decay, mechanical contact among bacterial cells, and adhesion between the bacteria and extracellular polymeric substances are incorporated. In addition, fluid-bacteria interaction is implemented to simulate biofilm deformation and erosion. The model predicts that the surface morphology of biofilms becomes smoother with increased nutrient concentration, which agrees well with previous literature. In addition, the results show that increased shear rate results in smoother and more compact biofilms. The model can also predict shear rate dependent biofilm deformation, erosion, streamer formation and breakup.

Utilizing a one-dimensional multispecies model to simulate the nutrient reduction and biomass structure in two types of H2-based membrane-aeration biofilm reactors (H2-MBfR): model development and parametric analysis

In this study, a one-dimensional multispecies model (ODMSM) was utilized to simulate NO3(-)-N and ClO4(-) reduction performances in two kinds of H2-based membrane-aeration biofilm reactors (H2-MBfR) within different operating conditions (e.g., NO3(-)-N/ClO4(-) loading rates, H2 partial pressure, etc.). Before the simulation process, we conducted the sensitivity analysis of some key parameters which would fluctuate in different environmental conditions, then we used the experimental data to calibrate the more sensitive parameters μ1 and μ2 (maximum specific growth rates of denitrification bacteria and perchlorate reduction bacteria) in two H2-MBfRs, and the diversity of the two key parameters' values in two types of reactors may be resulted from the different carbon source fed in the reactors. From the simulation results of six different operating conditions (four in H2-MBfR 1 and two in H2-MBfR 2), the applicability of the model was approved, and the variation of the removal tendency in different operating conditions could be well simulated. Besides, the rationality of operating parameters (H2 partial pressure, etc.) could be judged especially in condition of high nutrients' loading rates. To a certain degree, the model could provide theoretical guidance to determine the operating parameters on some specific conditions in practical application.

A Mixed-Culture Biofilm Model with Cross-Diffusion

We propose a deterministic continuum model for mixed-culture biofilms. A crucial aspect is that movement of one species is affected by the presence of the other. This leads to a degenerate cross-diffusion system that generalizes an earlier single-species biofilm model. Two derivations of this new model are given. One, like cellular automata biofilm models, starts from a discrete in space lattice differential equation where the spatial interaction is described by microscopic rules. The other one starts from the same continuous mass balances that are the basis of other deterministic biofilm models, but it gives up a simplifying assumption of these models that has recently been criticized as being too restrictive in terms of ecological structure. We show that both model derivations lead to the same PDE model, if corresponding closure assumptions are introduced. To investigate the role of cross-diffusion, we conduct numerical simulations of three biofilm systems: competition, allelopathy and a mixed system formed by an aerobic and an anaerobic species. In all cases, we find that accounting for cross-diffusion affects local distribution of biomass, but it does not affect overall lumped quantities such as the total amount of biomass in the system.

Experimental and Computational Investigation of Biofilm Formation by Rhodopseudomonas palustris Growth under Two Metabolic Modes

We examined biofilms formed by the metabolically versatile bacterium Rhodopseudomonas palustris grown via different metabolic modes. R. palustris was grown in flow cell chambers with identical medium conditions either in the presence or absence of light and oxygen. In the absence of oxygen and the presence of light, R. palustris grew and formed biofilms photoheterotrophically, and in the presence of oxygen and the absence of light, R. palustris grew and formed biofilms heterotrophically. We used confocal laser scanning microscopy and image analysis software to quantitatively analyze and compare R. palustris biofilm formation over time in these two metabolic modes. We describe quantifiable differences in structure between the biofilms formed by the bacterium grown heterotrophically and those grown photoheterotrophically. We developed a computational model to explore ways in which biotic and abiotic parameters could drive the observed biofilm architectures, as well as a random-forest machine-learning algorithm based on structural differences that was able to identify growth conditions from the confocal imaging of the biofilms with 87% accuracy. Insight into the structure of phototrophic biofilms and conditions that influence biofilm formation is relevant for understanding the generation of biofilm structures with different properties, and for optimizing applications with phototrophic bacteria growing in the biofilm state.

Cellular automata-based modelling and simulation of biofilm structure on multi-core computers

The article presents a mathematical model of biofilm growth for aerobic biodegradation of a toxic carbonaceous substrate. Modelling of biofilm growth has fundamental significance in numerous processes of biotechnology and mathematical modelling of bioreactors. The process following double-substrate kinetics with substrate inhibition proceeding in a biofilm has not been modelled so far by means of cellular automata. Each process in the model proposed, i.e. diffusion of substrates, uptake of substrates, growth and decay of microorganisms and biofilm detachment, is simulated in a discrete manner. It was shown that for flat biofilm of constant thickness, the results of the presented model agree with those of a continuous model. The primary outcome of the study was to propose a mathematical model of biofilm growth; however a considerable amount of focus was also placed on the development of efficient algorithms for its solution. Two parallel algorithms were created, differing in the way computations are distributed. Computer programs were created using OpenMP Application Programming Interface for C++ programming language. Simulations of biofilm growth were performed on three high-performance computers. Speed-up coefficients of computer programs were compared. Both algorithms enabled a significant reduction of computation time. It is important, inter alia, in modelling and simulation of bioreactor dynamics.